...Triangle cut by Lines Parallel to the Bafe being ("by 2. 6. Eucl. El.) proportional ; E С --ЕВ >; FA - FG; that is in Words, half the Sum of the Legs,...difference, as the Tangent of half the Sum of the oppofice Angles, is to the Tangent of half their difference; Fer i Sum -(- •', difference of any...

...Tangent of half their Difference. But Wholes are as their Halves : Therefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of...Angles, is to the Tangent of half their Difference. Which was, &c. From this Axiom the following Cafes will eafily be folved. CASE HI. Two Sides, with...

...Lines parallel to the Bafe being (by Eucl. 2. 6.) proportional as E С : С В :: FA : FG, »hat is, half the Sum of the Legs is to half their Difference, as the Tangent of halt the Sum of the oppofite Angles is to the Tangent of half their Difference : but Wholes are as...

...the observed angles PSY and PYS, we have, the tangent of half the sum of the first, to the tangent of half their difference, as the tangent of half the sum of the second, to tangent of 2° 54' 25"-9^i their half difference : from which we get the greater angle at...

...opposite side, or base, the cotangent of half the sum of the angles at the base will be to the tangent of half their difference, as the tangent of half the sum of the segments of the vertical angle is to the tangent of half their difference; that is, cot. | (A + B)...

...that is, The tangent of half the sum of any two sides of a spherical triangle is to the tangent of half their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 38. In the following articles it is proposed...